BRUSSELS/MOSCOW, June 2 (Reuters) - Russia's envoy to NATO on Monday accused the Western alliance of encouraging the use of force by the Ukrainian government in eastern Ukraine and of hampering efforts to find a peaceful solution to the crisis, Russian news agency RIA reported.

RIA quoted Alexander Grushko, who met ambassadors of NATO member states in Brussels, as saying "unprecedented" activity by the alliance near Russia's borders was adding to tension and could undermine existing security arrangements.

At a meeting that showed the sides were "far apart" on the Ukraine crisis, which has brought ties to a post-Cold War low, NATO envoys accused Russia of backing armed rebels in Ukraine, an alliance spokeswoman said.

NATO suspended all practical cooperation with Russia in April to protest its annexation of Crimea, but left the door open to contacts at ambassadorial level or higher in order to allow the two sides to discuss ways out of the crisis.

The Western military alliance has sought to reassure eastern European allies alarmed by Russia's takeover of Crimea by stepping up exercises and sending more fighter aircraft and ships to the region.

"We have noticed unprecedented NATO activity near Russia's borders. It is excessive, inappropriate, and weakens stability, security and predictability in the Euro-Atlantic region," state-run RIA quoted Grushko as saying.

He said that "demonstrations of military muscle and calls for increased military spending" were "a dead-end street. These actions are fraught with increased tension ... and the erosion of the existing security system in the region."

Ukrainian President-elect Petro Poroshenko and the pro-Western authorities in Kiev have defied Russia's calls for an end to the government's military operation against pro-Russian separatists in eastern Ukraine.

"NATO is providing Kiev ... with technical support, thus encouraging the continuation of forceful actions," Grushko was quoted as saying, adding that the alliance shared the blame for "the escalation of the situation" in eastern Ukraine.

A NATO spokeswoman said that at the meeting in Brussels "it was very clear that the views on the crisis in Ukraine remain far apart and NATO allies repeated their very strong and clear position on the illegal and illegitimate annexation of Crimea."

The NATO allies commended Ukraine's May 25 presidential election as a clear vote for the unity of the country and urged Russia to "engage constructively" with Poroshenko, said the spokeswoman, Oana Lungescu.

They also called on Russia "to stop the flow of arms and weapons across the border, to stop supporting armed separatists in Ukraine and to withdraw in a full and verifiable manner their troops from the Ukrainian border," she said.

Russia denies arming the rebels or orchestrating the unrest, and accuses Ukraine of aggravating the situation by resorting to force.

"Towards the end of his response, Ambassador Grushko said that he felt that we were talking about two different worlds, and that was very much my sensation too," a senior NATO diplomat said.

"The rhetoric is very inflammatory. It does not resemble the picture that we have of the situation in Ukraine, sadly, and it makes it very difficult for anyone to connect with this Russian world view." (Writing by Steve Gutterman; Editing by Mark Trevelyan)